Research Of Primitive Polynomial In Pseudorandom Sequences

Pseudorandom sequences have wide applications in simulation, software testing, global positioning systems, code division multiple-access systems, radar systems, spread-spectrum communication systems, and stream ciphers. Its technical base is to get the primitive polynomial. There are many ways to find the primitive polynomial, but it is difficult. According to the mode of cellular automata and some relative algebraic theories, the primitive polynomial in the binary field is searched quickly through MATLAB. It is easy and convenient to get the matrix by the maple's data package in the MATLAB.The inversed state transition matrix is usually used to estimate whether a polynomial is primitive or not, but we use the three diagonal matrixes. It needs to change the regular numbers in the diagonal to get different matrixes. Because the three diagonal matrixes is symmetrical, it saves much time in operating the procedure. At the same time, it can get large regular numbers that are satisfactory with the ruler. It is benefit for the research in the compensative cellular automata.The feedback function has been built up by the primitive polynomial. It can get much more m-sequences and pseudorandom sequences. The m-sequence is the longest period and its application is also wide. We introduce three ways to get the m-sequence: the ways of divert matrix, division and primitive polynomial. Comparing with the three ways, the way of primitive polynomial is best in the speed.